Question

Show that if a ray of light is reflected successively form two mirrors inclined at an angle $\theta$, the deviation of the ray does not depend upon the angle of incidence.

Answer 1

If ${\delta }_1$ and ${\delta }_2$ are the deviations suffered at $M_1$ and $M_2$ respectively, then ${\delta }_1=\pi -2i$ and ${\delta }_2=\pi -2i^{{}^{\prime }}$
Total deviation, $\delta =2\pi -2(i+i^{{}^{\prime }})$
From $\Delta OAB,\theta +\frac{\pi }{2}-i^{{}^{\prime }}+\frac{\pi }{2}-i=\pi or\theta =i^{{}^{\prime }}+i$
$\therefore \delta =2\pi -2\theta$
Thus, the total deviation is independent of angle of incidence.